Molecular Dynamics Study of the Effect of Chemical ...pdfs.semanticscholar.org/de03/5f8fb02edb6552a33c0d... · ical/molecular mechanics (QM/MM) calculations.15 Fur-thermore, a theoretical

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Copyright © 2010 American Scientific PublishersAll rights reservedPrinted in the United States of America

Journal ofNanoscience and Nanotechnology

Vol. 10, 1–5, 2010

Molecular Dynamics Study of theEffect of Chemical Functionalization on the

Elastic Properties of Graphene Sheets

Qingbin Zheng, Zhigang Li, Yan Geng, Shujun Wang, and Jang-Kyo Kim∗

Department of Mechanical Engineering, The Hong Kong University of Science and Technology,Clear Water Bay, Kowloon, Hong Kong, China

In this study, the effects of chemical functionalization on the elastic properties of graphene sheetsare investigated by using molecular dynamics (MD) and molecular mechanics (MM) simulations. Theinfluences of the degree of functionalization, which is defined as the ratio of the number of the totalsp3-hybridized atoms to the number of the total carbon atoms of the graphene sheet, the chiralityof graphene sheets, the molecular structure and molecular weight of functional groups on Young’smodulus are studied. The dependence of shear modulus and wrinkling properties on the functionalgroups are also investigated. The simulation results indicate that Young’s modulus depends stronglyon the degree of functionalization and the molecular structure of the functional groups, while theeffects of chirality of the graphene sheets and the molecular weight of the functional groups arenegligible. The chemical functionalization also reduces the shear modulus and critical strain, beyondwhich the wrinkling instability occurs.

Keywords: Graphene Sheet, Chemical Functionalization, Young’s Modulus, Shear Modulus,Critical Wrinkling Strain.

1. INTRODUCTION

Graphene sheets (GS) were officially defined in 1993 butfirstly produced in 2004.1 Their unique mechanical, ther-mal and electrical properties could have numerous poten-tial applications.2�3 Due to the high flexibility and largeinterfacial area, graphene can be a good candidate ofnanofiller to enhance the mechanical, thermal, and electri-cal properties of composite materials, such as commonlyused polymer matrix.4�5 Similar to carbon nanotube (CNT)based nanomaterials, the key challenges in the synthesisand processing of GS/polymer composites are the aggre-gation of GS and poor GS-polymer interactions.6�7 Oneeffective way to improve the dispersibility of GS and inter-facial bonding between GS and the supporting matrix is tofunctionalize the GS with certain chemical groups beforethey are dispersed into the matrix. The functional groups,however, may affect the mechanical and physical proper-ties of the GS and composites. Unfortunately, how chem-ical functionalizatioin affects the mechanical properties ofGS is unclear.The elastic properties of pristine graphene have

been recently determined by atomic force microscope

∗Author to whom correspondence should be addressed.

nanoindentations, which show that the graphene appears tobe the strongest material ever.8�9 The mechanical proper-ties of single GS, however, are not easy to be measured byexperiments. As a popular numerical approach, moleculardynamics (MD) simulations can be used to investigate themechanical properties of GS. The buckling, deformation,Young’s and shear moduli of GS have been obtained usingatomistic simulations.10–14 The effects of large defects andcracks on the mechanical properties of CNTs and GShave also been investigated by coupled quantum mechan-ical/molecular mechanics (QM/MM) calculations.15 Fur-thermore, a theoretical framework of nonlinear continuummechanics for graphene and a new formula of elastic bend-ing modulus for monolayer grapheme have been developedrecently as well.16 However, most of the previous studieshave been focused on pristine GS, the effect of chemicalfunctionalization on the elastic properties of GS has notbeen studied. For practical applications, it is necessary tounderstand the influence of certain functional groups onthe mechanical properties of GS.In this study, we investigate the effects of chemical func-

tionalization on the elastic properties of GS through MDand MM simulations. The force field of the condensed-phase optimized molecular potential for atomistic simula-tion studies (COMPASS) is used to model the interatomic

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interactions. Specifically, we study the effects of GS chi-rality, degree of functionlization, molecular structure andweight of functional groups on Young’s modulus of GS. Inaddition, the shear modulus and wrinkling properties arealso examined.

2. EXPERIMENTAL DETAILS

In this work, the MD and MM simulations are carried outusing Materials Studio developed by Accelrys Inc. TheCOMPASS module, which has been widely employed forvarious gas and condensed phase properties of many pop-ular organic and inorganic materials,17 is used to conductthe computations.The electronic structures of all the carbon atoms in the

graphene models are sp2-hybridization. The unsaturatedboundary effect is avoided by adding hydrogen atoms onthe edges of the GS. A pristine graphene sheet contain-ing 1372 carbon atoms and a graphene sheet functional-ized with 88 carboxyl functional groups in the center areshown in Figure 1. The simulations are carried out in the(N , V , T ) ensembles. The temperature of the system is

(a)

(b)

Fig. 1. Molecular models employed in the simulations. (a) A pristineGS (L0 = 5�823 nm, L1 = 5�904 nm). (b) A functionalized GS with88 carboxyl functional groups (top and side views).

set to be 1 K such that the thermal effect is avoided. Noperiodic boundary conditions are used for the pristine andfunctionalized GS and the time step is 1 fs. All the mea-surements are made after the systems reach equilibrium,which is achieved through a minimizer processor.18

To obtain Young’s modulus, the boundary carbon atomson the bottom side of GS are constrained and a positivedisplacement is applied to the boundary carbon atoms onthe top side. Young’s modulus is given by

E = 1V

�2U

�2�(1)

where E is Young’s modulus, V is the volume of the GS,U is the strain energy, and � is the strain. By changingthe displacement of the carbon atoms on the top side, thestrain energy and the corresponding strain of the GS aremeasured and their relationship is obtained by polynomialfittings.19 Young’s modulus is then determined throughEq. (1). Using similar approach, we shall also study theshear modulus and wrinkling properties of GS. The shearmodulus is estimated by the gradient of stress-strain curve.The critical wrinkling strain is obtained by increasing thedisplacement of the carbon atoms on the top side untilwrinkling occurs.

3. RESULTS AND DISCUSSION

3.1. Effect of Chirality on Young’s Modulus

The chirality of GS is related to their structure. For exam-ple, zigzag GS correspond to zero degree chiral angleand armchair GS correspond to a chiral angle of 30�.Figure 2(a) shows the curves of the strain energy and ten-sile load for zigzag and armchair GS. The Young’s mod-ulus of armchair GS is 1.086 TPa, which is a slightlylarger than that of zigzag GS (1.050 TPa). By changingthe chiral angle from 0� (zigzag) to 30� (armchair), westudy the effect of chirality on Young’s modulus, which isdepicted in Figure 2(b). The results confirm that Young’smodulus is not sensitive to the chirality of GS. Particu-larly, the effect of chirality is much weaker for large chi-ral angles. As shown in Figure 1(a), the graphene sheetis composed of interconnected hexagons of carbon atoms,which is highly symmetric. The fundamental hexagonalstructure makes the GS quite independent of the directionof tensile force. That is why similar Young’s modulus isobtained with different axial forces.

3.2. Effect of Degree of Functionalization onYoung’s Modulus

The chemical functionalization of GS has been performedby attaching different numbers of functional groups on thesurfaces of the GS line by line through covalent bonding.The number of functional groups will be equal to that ofthe sp3-hybridized carbon atoms on the surface of the GS.

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0 2 4 6 8 100

3000

6000

9000

12000

Armchair graphene E=1.086 TPa

Zigzag graphene E=1.050 TPa

Str

ain

ener

gy (

Kca

l/mol

)

Strain (%)

(a)

0 5 10 15 20 25 301035

1050

1065

1080

1095

Chiral angel (°)

Youn

g's

mod

ulus

(G

Pa)

(b)

Fig. 2. Effect of chirality on the Young’s modulus of GS. (a) Strainenergy-strain curve of armchair and zigzag GS. (b) Young’s modulus ofGS as a function of chiral angel.

0 2 4 6 8 100

3000

6000

9000

12000

Str

ain

ener

gy (

Kca

l/mol

)

Strain (%)

s = 3.207%, E = 0.982 TPas = 6.414%, E = 0.965 TPas = 9.621%, E = 0.727 TPas = 12.828%, E = 0.678 TPas = 16.035%, E = 0.607 TPa

(a)

0 4 8 12 160.20

0.25

0.30

0.35

0.40

0.45

0.50

Ave

rage

dis

plac

emen

t (an

gstr

om)

Degree of functionalization (%)

(b)

Fig. 3. Effect of degree of chemical functionalization on Young’s mod-ulus of GS. (a) Strain-strain energy curves of functionalized GS with dif-ferent degrees of functionalization (s is the degree of functionalization),(b) Average perpendicular displacement of the carbon atoms that linkedto the functional groups with different degrees of functionalization.

The degree of functionalization is defined as the ratio ofthe number of the total sp3-hybridized carbon atoms to thenumber of the total carbon atoms of the GS.Figure 3(a) shows the strain energy-strain curves for

different degrees of functionalization with carboxyl beingthe functional groups. It is seen that Young’s modulusdecreases rapidly with increasing degree of functionaliza-tion. Young’s modulus is reduced by about 42.2% whenthe GS are functionalized at a degree of functionalizationof 16%. The reduction in Young’s modulus is caused bythe structure change in the GS induced by the functionalgroups. As shown in the inset of Figure 3(b), the carbonatoms that are sp3-hybridized with functional groups arepulled away from the original plane of GS such that theGS are relatively in a more unstable state compared withthe pristine GS. In this case, it becomes easier to deformthe functionalized GS than the pristine GS. This is whyYoung’s modulus decreases as the degree of functionaliza-tion is increased. The average perpendicular displacementsof carbon atoms from the GS plane under different degreesof functionalization are shown in Figure 3(b), which areconsistent with the dependence of Young’s modulus on thedegree of functionalization shown in Figure 3(a).

3.3. Effect of Molecular Structure and Weight ofFunctional Groups on Young’s Modulus

Different functional groups may affect the Young’s mod-ulus of GS in different ways. To understand the effect of

3 4 5 6 7 8 9 100.75

0.80

0.85

0.90

0.95

1.00

Youn

g's

mod

ulus

(T

Pa)

Degree of functionalization (%)

–CH2–O–OH

–C3H

7 –N(CH

3)2

–COOH

(a)

20 40 60 800.75

0.80

0.85

0.90

0.95

1.00

Youn

g's

mod

ulus

(T

Pa)

(b)

Molecular weight

Fig. 4. Effects of molecular structure (a) and molecular weight (b) offunctional groups on Young’s modulus of GS.

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molecular structure, four functional groups with similarmolecular weight, alkyl hydroperoxide (–CH2–O–OH, 43),propyl (–C3H7, 43), dimethylamine (–N(CH3�2, 44), andcarboxyl (–COOH, 45) are identified. Figure 4(a) showsYoung’s modulus of functionalized GS. It is found thatYoung’s modulus is increasingly sensitive to the structureof the functional groups as increasing degree of functional-ization. Among the four groups, carboxyl affects Young’smodulus more than the other three groups, but the quali-tative dependence of Young’s modulus on the structure offunctional group remains the same regardless of the degreeof functionalization. We further investigate the effect ofmolecular weight on Young’s modulus. Six alkyl groupswith increasing molecular weight (–CH3, 15; –C2H5, 29;–C3H7, 43; –C4H9, 57; –C5H11, 71; –C6H13, 85) are cho-sen as the functional groups. Figure 4(b) shows that GSfunctionalized with the six different alkyl groups have sim-ilar Young’s modulus, which is about 0.85 TPa. Theseresults indicate that Young’s modulus depends strongly onthe molecular structure rather than the molecular weightof the functional groups. This is reasonable because thecovalent bonding between the carbon atoms and functionalgroups depends more on the structure of the function groupthan the molecular weight. It is the covalent bonding thatchanges the structure of GS (inset of Fig. 3(b)). Therefore,Young’s modulus is more sensitive to the structure thanthe molecular weight of the functional groups.

0 1 2 3 4 5 6 7

0

4

8

12

16Pristine grapheneG = 284 GPa7.5% –OH groupsG = 166 GPa

Str

ess

(GP

a)

Strain (%)

(a)

(b)

Fig. 5. Stress-strain curve under shear strain (a, G is the shear modulus)and wrinkling structure (b) of pristine GS.

3.4. Shear Modulus and Wrinkling Properties

Shear modulus is another important mechanical propertyof GS. Figure 5(a) shows the stress-strain curves from theshear displacement of pristine GS and GS functionalizedwith 7.5% –OH groups. The shear modulus of the GS isdetermined by the slope of the stress-strain curve. It is seenthat the functional groups reduce the shear modulus. Thecritical wrinkling strain, at which the winkling instabilitytakes place, can be obtained by further increasing the shearstrain. The critical wrinkling strains for pristine GS andGS functionalized with 7.5% –OH groups are about 6%and 4.5% respectively, which shows that chemical func-tionalization also results in a lower critical wrinkling. Thewrinkling mode of a pristine graphene is illustrated inFigure 5(b). Similar to Young’s modulus, this degradedshear stiffness is caused by the attached functional groups,with which the GS are in a relatively less stable state.

4. CONCLUSIONS

In this study, the effects of chemical functionalizationon the mechanical properties, including Young’s modu-lus, shear modulus, and wrinkling properties, are inves-tigated based on MD and MM simulations. It is foundthat Young’s modulus depends strongly on the degreeof functionalization and molecular structure of the func-tional groups, while the effects of chirality of the GS andmolecular weight of the functional groups are unimpor-tant. The chemical functionalization also reduces the shearmodulus and the critical wrinkling strain. The simulationresults indicate that although chemical functionalization ofGS has been considered as an effective way to increaseload transfer efficiency in GS/polymer composites,5 atten-tions should be paid to the weakened elastic stiffness dueto the attachment of functional groups.

Acknowledgments: This work was supported by theResearch Grant Council of Hong Kong SAR and HenkelInternational, formerly Imperial Chemical Industries Ltd.(Project No. ICIPLC001.07/08).

References and Notes

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Received: 4 September 2009. Accepted: 30 October 2009.

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